YCWM Warananagar

1. Department of Physics
B.SC.III
Sem-V.Paper-XII
DSE-E4- Digital and Analog Circuits and Instrumentation
Topic-Oscillator

2. Oscillator is an electronic circuit which converts dc
energy into an ac energy at a very high frequency.
Oscillator is an electronic source of alternating current
or voltage, it is periodically varying electrical output.
Which is having sine, square or saw-tooth shapes. It is a
circuit which generates an ac signal without requiring
any externally applied input signal. Oscillator is basically
an amplifier, but slightly different from that. Block
diagram of oscillator is shown in fig.
Basic Oscillator Circuit.
In amplifier circuit the frequency , waveform and
amplitude of a.c. generated output is controlled by an
a.c. signal voltage applied.
While in an oscillator the frequency , waveform and
amplitude of a.c. generated output is
controlled by circuit itself.
Amplifier : An amplifier produces an output signal whose
waveform, frequency and amplitude is depend on the
waveform, frequency and amplitude of input signal. For
amplifier additional power is supplied by external dc source.
Fig.
Oscillator : In case of oscillator, the waveform, frequency and
amplitude of output signal depends on the circuit itself.
Oscillator does not require an external signal to start or
maintain energy conversion process. It keeps producing an
output signal, so long as dc power source is connected.

3. The basic oscillator concept shows the following types of
waveforms – (I) Sine wave (II) Square wave (III)
Triangular wave (IV) Saw-tooth wave
: These oscillators produce sine wave at
the o/p when they are turned on. The waveform at the
output is shown. The fundamental function for this
oscillator is V = 𝑉𝑚 𝑠𝑖𝑛𝑤𝑡,
𝑤ℎ𝑒𝑟𝑒 𝑉𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑎𝑥 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑜𝑢𝑡𝑝𝑢𝑡𝑠𝑖𝑔𝑛𝑎𝑙
: These oscillators produce square
wave at the output. The fundamental function for this
oscillator is
𝑉 =
𝑉
𝑚 𝑓𝑜𝑟 𝑇 = 0 𝑡𝑜
𝑇
2
0 𝑓𝑜𝑟 𝑇 =
𝑇
2
𝑡𝑜 𝑇
: These oscillators produce
triangular wave at the output. The fundamental function for
this oscillator is
V=
𝑒𝑥 𝑓𝑜𝑟 𝑇 = 0 𝑡𝑜
𝑇
2
1 − 𝑒𝑥
𝑓𝑜𝑟 𝑇 =
𝑇
2
𝑡𝑜 𝑇
0 𝑓𝑜𝑟 𝑇 = 0

4. The basic oscillator concept shows the following types of
waveforms – (I) Sine wave (II) Square wave (III)
Triangular wave (IV) Saw-tooth wave
: These oscillators produce sawtooth
wave at the output. The fundamental function for this
oscillator is
𝑉 =
𝑒𝑥
𝑓𝑜𝑟 𝑇 = 0 𝑡𝑜 𝑇
0 𝑓𝑜𝑟 𝑇 = 0 𝑇 = 𝑇

5. :The process
of injecting a fraction of output energy of
some device back to the input is known as
feedback. Feedback is useful to reduce the
noise in amplifier. It also makes amplifier
operation stable. Depending upon whether
the feedback energy aids or opposes the input
signal, there are two basic types of feedback
viz, positive feedback and negative feedback.
: When the feedback
energy (voltage or current) is in phase with the input
signal and thus aids it, it is called positive feedback.
Both amplifier and feedback network introduce a
phase shift of 180°. It causes a 3600phase shift around
the loop which causes the feedback voltage Vf to be in
phase with the input signal Vm.
The positive feedback increases the
gain of the amplifier. But positive
feedback increases distortion and
instability. Therefore, positive feedback
is rarely employed in amplifiers.
Important use of positive feedback is in
oscillators.

6. When the feedback energy
(current or voltage) is out of phase with the input
signal and thus opposes it, it is called negative
feedback. shows that the amplifier introduces a
phase shift of 1800 into the circuit. Here feedback
network is designed in such a way that it
introduces no phase shift (0° phase shift). So the
feedback voltage Vf is 180° out of phase with the
input signal V. Negative feedback reduces the
gain of the amplifier.
Advantages of Negative Feedback :
(i) Reduction in distortion
(ii) Stability in gain (iii) Increased Bandwidth
(iv) Improved input and output impedances.
Because of these advantages, the negative
feedback is frequently employed in amplifiers.

7. In feedback oscillator we know that a part of output signal can be fed back
to the input with help of feedback network , if positive feedback is used.
In case of positive feedback, the feedback voltage is in phase with the
input voltage. 𝑉𝑖 and 𝑉𝑓are added up to make 𝑉𝑖
′
. 𝑉𝑖
′
=
𝑉𝑖+ 𝑉𝑓 = 𝑉𝑖 + 𝛽𝑉0
′
Where 𝑉𝑓 = 𝛽𝑉0
′
and 𝛽 − 𝑖𝑠 𝑡ℎ𝑒 𝑓𝑒𝑒𝑑 𝑓𝑎𝑐𝑡𝑜𝑟
or feed fraction 𝐺𝑎𝑖𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑎𝑠𝑖𝑐 𝑎𝑚𝑝𝑙𝑖𝑓𝑖𝑟𝑒 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑓𝑒𝑒𝑑𝑏𝑎𝑐𝑘 = 𝐴𝑣 =
𝑉0
′
𝑉𝑖
′
∴ 𝑉𝑖
′
=
𝑉0
′
𝐴𝑣
= 𝑉𝑖 + 𝛽𝑉0
′
∴ 𝑉0
′
= 𝐴𝑣 𝑉𝑖 + 𝛽𝑉0
′
=𝐴𝑣𝑉𝑖 + 𝐴𝑣𝛽𝑉0
′
𝑉0
′
− 𝐴𝑣𝛽𝑉0
′
= 𝐴𝑣𝑉𝑖
∴ 𝑉0
′
1 − 𝐴𝑣𝛽 = 𝐴𝑣𝑉𝑖
𝑉0
′
𝑉𝑖
= 𝐴𝑣𝑓 =
𝐴𝑣
1 − 𝐴𝑣𝛽
𝐴𝑣𝑓is the gain of amplifier with feedback. 𝐴𝑣𝑓 is always greater than
𝐴𝑣. Therefore, positive feedback is obtained.
Now when 𝛽 is negative gain reduces But if it is positive the gain is
increases. To how much extent it is increases depends upon how
much feedback is introduced consider following examples.
In which 𝐴𝑣=40 and 𝛽=0.01, 0.02, 0.025
Now for 𝛽=0.01; 𝐴𝑣𝑓 =
𝐴𝑣
1−𝐴𝑣𝛽
=
40
1−(40𝑥0.01)
=
40
0.6
=66.66.
Now for 𝛽=0.02; 𝐴𝑣𝑓 =
𝐴𝑣
1−𝐴𝑣𝛽
=
40
1−(40𝑥0.02)
=
40
0.2
= 200.
Now for 𝛽=0.025; 𝐴𝑣𝑓 =
𝐴𝑣
1−𝐴𝑣𝛽
=
40
1−(40𝑥0.025)
=
40
0
=∞.
This shows that the gain will increase with a larger amount of
feedback until a critical stage is reached. At this stage the gain is
infinite. At this stage the gain is infinite, but the output can not be
infinite. It mean that at this stage output voltage will be developed
without input. Here the circuit stops amplifying and starts oscillating.
Its frequency depend on feedback network of amplifier.

8. The positive feedback increases gain of amplifier. At the particular
value of 𝛽 it becomes ∞ and circuit becomes oscillator. We have
the relation for gain with feedbacks- This gives the condition under
which a feedback amplifier can work as an oscillator. For an amplifier
with positive feedback, the voltage gain is given by where
𝐴𝑣𝑓 =
𝐴𝑣
1−𝐴𝑣𝛽
=
𝑉0
′
𝑉𝑖
, 𝐴𝑣𝑓- gain of amplifier with feedback𝐴𝑣 -
gain of basic amplifier without feedback.𝛽 - feedback factor𝐴𝑣𝛽-
Loop gain, If 𝐴𝑣𝛽 = 1, 𝐴𝑣𝑓=∞. 𝐴𝑣𝑓=
𝑉0
′
𝑉𝑖
∴ as 𝐴𝑣𝑓 =∞,
𝑒𝑣𝑒𝑛 𝑤ℎ𝑒𝑛 𝑉𝑖 = 0 𝑎𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 𝑉0
′
𝑐𝑎𝑛 𝑏𝑒 𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑. ∴ 𝐴𝑣𝛽 =
1, a feedback amplifier can act as an oscillator,
This is known as Barkhausen criterion. here we get three
conditions 1. if loop gain 𝐴𝑣𝛽 < 1, then product (𝐴𝑣𝛽.V𝑜) will be less
than V𝑜 and output will die as shown in fig.1. such oscillations are
called as damped oscillations. This happen when enough energy is
not returned to input. 2. if loop gain 𝐴𝑣𝛽 > 1, then product
(𝐴𝑣𝛽.V𝑜) will be appears greater than V𝑜 and output will builds up
shown in fig.2. such oscillations are called as growing oscillations.
This happen when extra energy is returned to input.
3. if loop gain 𝐴𝑣𝛽 = 1, then product (𝐴𝑣𝛽.V𝑜)= V𝑜 no change is occur in output
and here we get output without input. We get output with constant amplitude
i.e. Sustained oscillations. shown in fig.3. here loop gain 𝐴𝑣𝛽=1 then 𝐴𝑣𝑓 =∞ i.e
gain with feedback becomes ∞ and it produces output without input. Here
amplifier becomes oscillator. Thus the conditions𝐴𝑣𝛽 = 1 or 𝛽 =
1
𝐴𝑣
which
converts amplifier in to oscillator and give sustained oscillations. Is called as
Barkhausen criterion for sustained oscillations.Conditions for Barkhausen
Criteria 1. 1 𝐴𝛽 = 1 2. Feedback signal should be in phase with input signal. If
𝐴𝛽 < 1 continuous oscillations are not produced. So in a practical circuit, loop
gain 𝐴𝛽 is kept slightly higher than one.

9. Oscillator Circuit(Tank Circuit)
Essential parts of Oscillator-1) Oscillatory Ckt, Transistor
Amplifire, Feedback circuit.
A circuit which produces
electrical oscillations of any desired frequency is known as
an oscillatory circuit. A simple oscillatory circuit consists of a
capacitor (C) and inductance coil (L) in parallel as shown in
Fig. 3.2. This electrical system can produce electrical
oscillations of frequency determined by the values of L and
C. Tank Circuit
(i) energy is introduced into the circuit by connecting a
capacitor to a dc voltage source. The upper plate of capacitor
has deficit of electrons and lower plate has excess of electrons.
There is a voltage across the capacitor and capacitor has
electrostatic energy. (ii) When switch S is closed as shown in
Fig. (ii), the capacitor will discharge through inductance and
the electron flow is indicated by the arrow. This current flow
sets up magnetic field around the coil. The circuit current is
maximum when capacitor is fully discharged. Here
electrostatic energy is converted into magnetic field energy
around the coil. (iii) Once the capacitor is discharged, the
magnetic field will collapse and produce a counter e.m.f. This
counter e.m.f. will keep the current flowing in the same
direction. So the capacitor is now charged with opposite
polarity shown in Fig. (iii).

10. (iv) Once the collapse field has recharged the capacitor, the capacitor
now begins to discharge and current flows in the opposite direction. Fig.
3.2 (iv) shows capacitor fully discharged and maximum current flowing.
The sequence of charge and discharge results in oscillating current. The
energy is alternately stored in the electric field of capacitor (C) and the
magnetic field of inductance coil (L). This interchange of energy between
L & C is repeated again which produces oscillations.
3.3.1 : Damped Oscillations : In a practical tank circuit, there are resistive
and radiation losses in the coil and dielectric losses in the capacitor.
During each cycle, a small part of the originally imported energy is used
to overcome these losses. So the amplitude of oscillating current
decreases and eventually it becomes zero. Therefore, the tank circuit will
produce damped oscillation shown in Fig. 3.3. Frequency of Oscillations :
The frequency of oscillations is the resonant frequency of the tank circuit.
𝐹 =
1
2𝜋 𝐿𝐶
: Damped Oscillations from tank circuit
where L —› self inductance in µH
C capacitance in µF
so the frequency of oscillations is inversely proportional to L &
C. If a larger value of capacitor is used, it will take longer
period for the capacitor to charge and discharge. This will
lengthen the period of oscillations in the tank circuit. Also larger
the self inductance, longer the time required to complete each
cycle.

11. : Undamped oscillations from Tank circuit : As
discussed above, the tank circuit produces
damped oscillations. These are not useful for
radio transmission because of their limited
range and excessive distortion. For good radio
transmission, we need undamped oscillations
which can be produced if some additional
energy is supplied in correct phase and correct
direction to the LC circuit to make up I2R
losses occurring in the circuit.
Undamped Oscillations from Tank Circuit As
discussed before, a tank circuit produces
damped oscillations.
However, in practice, we need continuous
undamped oscillations for the successful
operation of electronics equipment.
In order we make the oscillations in the tank
circuit undamped, it is necessary to supply
correct amount of energy to the tank circuit at
the proper time to meet the losses. Thus
referring back to Fig. 3.3 any energy which
would be applied to the circuit must have a
polarity conforming to the existing polarity at
the instant of application of energy. If the
applied energy is of opposite polarity, it would
oppose the energy in the tank circuit, causing
stoppage oscillations. Therefore, in order to
make the oscillations in the tank circuit
undamped, the follows conditions must be
fulfilled

12. Undamped oscillations
• (i) The amount of energy supplied
should be such so as to meet the losses
in the tank circuit and the a.c. energy
removed from the circuit by the load.
For instance, if losses in LC circuit
amount to 5mW and a.c. output being
taken is 100mW, then power of 105mW
should be continuously supplied to the
circuit. (ii) The applied energy should
have the same frequency as that of the
oscillations in the tank circuit. (iii) The
applied energy should be in phase with
the oscillations set up in the tank circuit
it should aid the tank circuit oscillations.
If these conditions are fulfilled, the
circuit will produce continuous
undamped output as shown in Fig.

13. Block diagram of oscillator Fig. () below shows
the block diagram of oscillator. Its essential
components are as below.
(A) Tank circuit : It consists of inductance coil (L)
connected in parallel with capacitor C. The
frequency of oscillations in the circuit depends
upon the values of inductance of the coil and
capacitance the capacitor.
• (B) Transistor amplifier : The transistor
amplifier receives d.c. power from the
battery and changes it into a.c. power for
supplying to tank circuit. The oscillations
occurring in the tank circuit are applied the
input of the transistor amplifier. Because of
the amplifying properties of the transistor,
we get increased output of these
oscillations. This amplified output of
oscillations is due to the d.c. power
supplied the battery. The output of the
transistor can be supplied to the tank
circuit to meet the losses. ‘
• (C) Feedback circuit : The feedback circuit
supplies a part of collector energy to the
tank circuit in correct phase to help the
oscillations.It provides the positive
feedback.

14. • An electronic device that generates sinusoidal
oscillations of desired Frequency is known as a
sinusoidal oscillator. Here though we speak of an
oscillator as "generating" a frequency, should it should
be noted that it does not create energy, but merely acts
as an energy converter. It receives d.c. energy and
changes it into a.c. energy of desired frequency. The
frequency of oscillations depends upon tconstants he is
of the device.
• Even though oscillations can also be produced by
mechanical devices like alternators, electronic
oscillators have many advantages. They are
n oscillator is a non rotating
device. Hence there is very less wear and tear. Thus it
has longer life.
• II)Due to absence of moving parts, the operation is quite
silent.
• (iii) An oscillator can produce frequencies from low (20
Hz) to very (> 100 MHz).
• (iv) The frequency of oscillations can be easily changed
when desired.
• (v) It has good frequency stability i.e. frequency once set
remains constant for a considerable period of time.
• (vi) It has very high efficiency.
• Sinusoidal oscillations are of two types. One is damped
oscillations and other is undamped or sustained
oscillations.